For the teaching of mathematics, particularly to beginning students in the lower grades, a number of devices have been proposed to help those students visualize the mathematical activity being taught. For example U.S. Pat. No. 4,894,973 is designed to aid in teaching of children to add and subtract. This device requires a teacher to place certain panels on the base of the unit after which the student can manipulate beads in response to the mathematical activity set up by the teacher.
In yet another device, shown in U.S. Pat. No. 5,205,744, a spaced series of U shaped rods are disposed on a base. The rods carry slidable counting beads on all but two of the rods. These two rods are provided with sign beads for indicating the mathematical function being performed. Manipulation of the beads allows students to visualize subtraction, addition, multiplication and division by seeing the number of beads on the rods involved in the mathematical operation.
These devices, although suitable for simple mathematical functions, are limited in their representations of mathematical functions. For example, they're unable to visually represent the result of the mathematical manipulation of two numbers unless the beads are first arranged by the instructor. Indeed, unless the instructor arranges the proper number of beads, the student is may not accurately arrive at and see the results of the mathematical functions being demonstrated. In addition, these devices are not sophisticated enough to demonstrate number theory and relationships.